Let X and Y be independent random variables with a discrete uniform distribution, i.e., with probability mass functions Use the addition rule for discrete random variables on page 152 to determine the...

Let X and Y be independent random variables with a discrete uniform distribution, i.e., with probability mass functions

Use the addition rule for discrete random variables on page 152 to determine the probability mass function of Z = X + Y for the following two cases.

a. Suppose N = 6, so that X and Y represent two throws with a die. Show that

You may check this with Quick exercise 11.1.

b. Determine the expression for pZ(k) for general N.